Properties of Binomial Distribution 📊

For a Binomial Distribution with parameters n and p:

1. Mean (μ)

The average number of successes expected.

Mean = n * p

2. Variance (σ²)

Measures the spread of the distribution.

Variance = n * p * q

(Since q < 1, Variance is always LESS than Mean in Binomial Distribution).

3. Standard Deviation (σ)

Standard Deviation = √(n * p * q)

4. Mode

Likeliest number of successes.

• Calculate k = (n + 1) * p.
• If k is an integer: Two modes, k and k-1.
• If k is not an integer: Mode is the integer part of k.

Summary Table 📋

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Example

If n = 10 and p = 0.4.

1. Mean: 10 * 0.4 = 4
2. Variance: 10 * 0.4 * 0.6 = 2.4
3. SD: √2.4 ≈ 1.55

(Check: Mean (4) > Variance (2.4). Correct.)

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